Answer:
D.
Step-by-step explanation:
1) the domain is x∈[0;+∞);
2) the solution is:

3) finally, the solution with the domain is:
x∈[0;100].
Answer:
the least integer for n is 2
Step-by-step explanation:
We are given;
f(x) = ln(1+x)
centered at x=0
Pn(0.2)
Error < 0.01
We will use the format;
[[Max(f^(n+1) (c))]/(n + 1)!] × 0.2^(n+1) < 0.01
So;
f(x) = ln(1+x)
First derivative: f'(x) = 1/(x + 1) < 0! = 1
2nd derivative: f"(x) = -1/(x + 1)² < 1! = 1
3rd derivative: f"'(x) = 2/(x + 1)³ < 2! = 2
4th derivative: f""(x) = -6/(x + 1)⁴ < 3! = 6
This follows that;
Max|f^(n+1) (c)| < n!
Thus, error is;
(n!/(n + 1)!) × 0.2^(n + 1) < 0.01
This gives;
(1/(n + 1)) × 0.2^(n + 1) < 0.01
Let's try n = 1
(1/(1 + 1)) × 0.2^(1 + 1) = 0.02
This is greater than 0.01 and so it will not work.
Let's try n = 2
(1/(2 + 1)) × 0.2^(2 + 1) = 0.00267
This is less than 0.01.
So,the least integer for n is 2
Answer:
B
Step-by-step explanation:
it is the opposite of A, which is true, as |-8| = 8
9514 1404 393
Answer:
2) true
3) X = -19/48
4) Y = 27/56
Step-by-step explanation:
3) Subtract 5/6 from both sides
X = 7/16 -5/6 = (7·6 -16·5)/(16·6) = (42 -80)/96
X = -19/48
__
4) Subtract 1/7 from both sides
Y = 5/8 -1/7 = (5·7 -8·1)/(8·7)
Y = 27/56
37:prime 65:composite 71:composite 82:composite